Maths topics, all in one place
Each topic gathers its lessons behind one page: what it is, how to solve it, the mistakes to avoid, and the questions students actually ask.
Maths topic guides
- Indices, Powers and RootsThe laws of indices, negative and fractional powers, square roots and standard form.6 min read
- Coming soonFractions and DecimalsEvery fraction operation, converting between the two, and recurring decimals.
- Coming soonFactors, Multiples and PrimesQuick digit checks for what divides exactly, breaking numbers into primes, and finding what two numbers share.
- Coming soonNumber BasicsPlace value and rounding, the order of operations, written methods for the four operations, and negative numbers.
- Coming soonSimultaneous EquationsTwo equations, two unknowns: solve them by graphing, substitution or elimination.
- Coming soonQuadratic EquationsFactorising, the quadratic formula and vertex form, and knowing which one a question wants.
- Coming soonStraight-Line Graphs and FunctionsPlotting lines, the equation of a straight line, and what m and c actually change.
- Coming soonSequencesFinding the nth term of a linear sequence, plus quadratic, geometric and Fibonacci sequences.
- Coming soonPercentages and InterestPercentage of a number, increase and decrease, percentage change, and simple and compound interest.
- Coming soonRatio and ProportionSplitting amounts into parts, linking two ratios into one, and telling quantities that rise together from ones that trade places.
- Coming soonCompound MeasuresSpeed, density and pressure on one formula triangle — and converting both halves of a unit like g/cm³.
- Coming soonAngles and PolygonsThe angle rules and facts, and the shapes they name — from parallel lines to quadrilaterals.
- Coming soonPythagoras and TrigonometryFinding missing sides and angles with Pythagoras, SOH CAH TOA, and the sine and cosine rules.
- Coming soonArea and PerimeterWhat each one measures, the formula for every basic straight-sided shape, and compound shapes.
- Coming soonTransformations and SymmetrySlide, flip, turn and resize a shape on a grid, describe any single transformation fully, and count what stays the same.
- Coming soonVolume and Surface AreaFilling the inside and covering the outside: boxes, prisms and cylinders, and the solids that narrow to a point.
- Coming soonProbabilityCalculating a probability, the addition rule and expected frequency, tree diagrams, and sets and Venn diagrams.
- Coming soonStatistics: Averages, Charts and TablesMean, median, mode and range, frequency tables, and every chart you need to read or draw.
Percentages and Interest
A percentage means “out of 100” — so 30% of something is 30 out of every 100 parts of it.
Every guide opens the same way: what the topic actually is, in plain English, before any method or formula turns up.
How to solve it
Each term is the last two added together
2571219the two starters
2 + 5 =75 + 7 =127 + 12 =19That’s a Fibonacci-type sequence. The famous one starts 1, 1 — but any two starting numbers work, and those two starters decide every term that follows.
Up to three named methods, each one solved step by step in a worked example and each backed by the one lesson that teaches it properly.
Key skills
Tick what you can already do:
- I can turn a percentage into a decimal by dividing by 100
- I can find 10% of a number by dividing by 10
- I can find any percentage of a number by multiplying by its decimal
- I can find the original value after a change by dividing by the multiplier
Can’t tick one of these? Ask ChatCat
The skills the exam actually tests, as a checklist you can tick off, so it is obvious what to practise next.
Common mistakes
The mistake
You turned 5% into 0.5.
What to do instead
Divide by 100: 5% = 0.05.
The mistake
You divided by 20 to find 20%.
What to do instead
Multiply by the decimal: 60 × 0.2 = 12.
The slips examiners see every year, each one paired with what to do instead.
FAQs
How do you work out VAT?
The UK’s standard rate is 20% — multiply the base price by 1.2.
What does per annum mean?
Can you work out percentages without a calculator?
The questions students really ask about the topic, answered straight.
Whatever the topic, personal maths support starts here.
Not sure yet? Try Maths Angel for free and see if it’s the right fit for your child.
No card needed